STRC02 ReinforcedConcrete Part2 0715

Structural Engineering Review Course

Reinforced Concrete Design (Part 2)

Reinforced Concrete Design (Part 2) Structural Engineering Review Course

STRC ©2015 Professional Publications, Inc.

© 2015 Professional Publications, Inc.

1



Reinforced Concrete Design

Lesson Overview Reinforced Concrete Design (Part 2) • Concrete Columns • Development and Splice Length of Reinforcement • Two‐Way Slab Systems • Anchoring to Concrete



2

2




Learning Objectives You will learn • R/C column design • R/C slab design • design of anchorage to concrete • how to avoid potential SE exam pitfalls • tricks to speed up problem solving on the exam



3

3




Prerequisite Knowledge You should already be familiar with • statics • mechanics of materials • structural analysis • basic reinforced concrete terminology • basic reinforced concrete design concepts • Reinforced Concrete Design (Part 1)



4

4




Referenced Codes and Standards • International Building Code (IBC, 2012) • Building Code Requirements for Structural Concrete (ACI 318, 2011) • Minimum Design Loads for Buildings and Other Structures (ASCE/SEI7, 2010) • Steel Construction Manual (AISC, 2011)



5

5




Example: Exam Strategy You’ve spent six minutes on a problem and you aren’t finished yet. You think you know the procedure to finish the problem, but it is going to take a few more minutes. What should you do? (A)Finish the problem. (B) Weed out a few choices if possible at this point and then guess. (C) Leave it blank and move on to the next problem.



6

6




Example: Exam Strategy You’ve spent six minutes on a problem and you aren’t finished yet. You think you know the procedure to finish the problem, but it is going to take a few more minutes. What should you do? (A)Finish the problem. (B) Weed out a few choices if possible at this point and then guess. (C) Leave it blank and move on to the next problem. The answer is (C). STRC ©2015 Professional Publications, Inc.


7

7




Concrete Columns ACI defines a column as • member with height‐to‐least lateral dimension ratio > 3 • used primarily to support axial compressive loads



8

8




Concrete Columns longitudinal reinforcement • minimum of 1% Ag • maximum of 8% Ag • for column with rectangular or circular ties, minimum of 4 longitudinal bars • for columns with spirals, minimum of 6 longitudinal bars



9

9




Concrete Columns transverse reinforcement spiral reinforcement requirements (ACI Sec. 7.10.4) •

minimum volume ratio,

•

1 in ≤ clear space ≤ 3 in

•

db,min = 3/8 in



10

10




Concrete Columns transverse reinforcement (continued) Fig. 1.17 Column Ties

tie reinforcement • minimum size no. 3 for longitudinal bars of no. 10 or smaller no. 4 for longitudinal bars larger than no. 10 • maximum spacing



11

11




Example: Concrete Columns CSCO Example 6.4



12

12







13

13




Example: Concrete Columns



14

14




Concrete Columns effective length

Fig. 1.18 Alignment Charts for k2

To use the chart, calculate the stiffness ratio at the end of the column.

For a non‐sway (braced) frame, may assume k = 1.0.



15

15




Concrete Columns slenderness ratio • slenderness ratio =

klu r

• k = effective length factor (1.0 or from charts) • lu = unsupported length of compression member •



16

16




Example: Concrete Columns Example 1.15

For this example, determine only the slenderness ratio of column 12.



17

17




Example: Concrete Columns Example 1.15

For this example, determine only the slenderness ratio of column 12.



18

18





Adapted with permission from Building Code Requirements for Structural Concrete and Commentary (ACI 318‐11) Fig. R10.10.1.1, copyright © 2011, by the American Concrete Institute STRC ©2015 Professional Publications, Inc.


19

19







20

20




Concrete Columns short column with axial load • column in sway frame is short column and slenderness ignored if • column in non‐sway is short column if • if column bent in single curvature, 34

ACI Eq. 10‐7

and M1/M2 are positive



ACI Eq. 10‐6

21

21




Concrete Columns design axial capacities for short columns • spiral reinforcement



 Pn  0.85 0.85 f c'  Ag  Ast   Ast f y



  0.75

ACI Eq. 10‐1



  0.65

ACI Eq. 10‐2

• tie reinforcement



 Pn  0.80 0.85 f c'  Ag  Ast   Ast f y



22

22







23

23







24

24







25

25




Concrete Columns short column with end moments Axial capacity decreases as end moments are applied. • For approximate values, see STRM App. C – App. H. • For refined values, use a computer (this can’t be covered on the exam).



26

26




Concrete Columns long column without sway requires consideration for secondary bending stresses (P‐delta) •

2nd order frame analysis (computer)

•

approximate method •

Perform 1st order analysis (standard analysis).

•

Multiply by moment magnifiers.

•

Design for axial + magnified moments with short column procedure.



27

27




Concrete Columns long column without sway (continued) • moment correction factor

• magnification factor ACI Eq. 10‐12

ACI Eq. 10‐16

• Euler critical load

• design for magnified moment ACI Eq. 10‐13

ACI Eq. 10‐11

• flexural rigidity ACI Sec. R10.10.6.2



28

28




Concrete Columns long column with sway • Combine non‐sway moments and magnified sway moments.

• magnification factor ACI Eq. 10‐21

ACI Eq. 10‐18 ACI Eq. 10‐19

Summations apply to all columns in a story.



29

29




Development and Splice Length of Reinforcement straight bars in tension general equation ACI Eq. 12‐1



30

30




Development and Splice Length of Reinforcement straight bars in tension (continued) transverse reinforcement index, Ktr



Fig. 1.19 Derivation of Ktr

31

31




Development and Splice Length of Reinforcement straight bars in tension (continued) excess reinforcement

bundled bars •

2‐bar bundle: same as individual bar

•

•

3‐bar bundle: individual bar development + 20%

• not applicable when full yield strength is required

•

4‐bar bundle: individual bar development + 33%



32

32



Reinforced Concrete Design Example: Development and Splice Length of Reinforcement CSCO Example 9.1



33

33



Reinforced Concrete Design Example: Development and Splice Length of Reinforcement



34

34






35

35




Development and Splice Length of Reinforcement straight bars in compression • calculate basic development length

• multiply by



36

36






37

37






38

38




Development and Splice Length of Reinforcement hooked bars in tension • basic development length

• for epoxy‐coated reinforcement

• for lightweight concrete

• multiply basic development, lhb, by additional factors



39

39




Development and Splice Length of Reinforcement hooked bars in tension (continued) additional factors • Cb = 0.7 for bars ≤ no. 11, with side covers ≥ 2.5 in, and end covers ≥ 2.0 in. (Otherwise, Cb = 0.1) •

for db ≤ 11 and ties at s ≤ 3db,

• excess reinforcement factor,



40

40




Development and Splice Length of Reinforcement hooked bars in tension (continued) For a hook at discontinuous end of member with cover < 2.5 in, ties are required over full development length at s ≤ 3db. minimum value for development length (after modifiers)



41

41






42

42






43

43






44

44




Development and Splice Length of Reinforcement curtailment of reinforcement

Fig. 1.20 Curtailment of Reinforcement

• length that reinforcement must extend beyond the theoretical cutoff point • not required at ends of simple support span • not required at end of cantilever



45

45




Development and Splice Length of Reinforcement curtailment of reinforcement (continued) At physical cutoff point, must also meet one of these conditions. •

Vu ≤ ⅔ϕVn

•

stirrups provided with minimum area of 60bws/fyt over distance 0.75d, spaced at s ≤ d/8βb

•

for #11 bars or smaller, continuing bars provide 2Mu and Vu ≤ ¾ ϕVn.



46

46



Reinforced Concrete Design Example: Development and Splice Length of Reinforcement A beam is made of 5 ksi concrete and is reinforced at midspan with four deformed #8 bars. The bars are not epoxy coated. The bars have 2 in of cover and 6 in of clear spacing. The effective depth of the beam is 24 in. The moment demand at 3 ft away from midspan is half of the demand at midspan. At what distance from midspan can 2 of the bars be terminated? (A) 36 in (B) 42 in (C) 48 in (D) 60 in



47

47



Reinforced Concrete Design Example: Development and Splice Length of Reinforcement Table 1.4 Values of ld/db for Grade 60 bars with Ψe = Ψt = λ = 1.0

option A 36 in = distance away from midspan that the moment is halved option B 42 in = development length from STRM Table 1.4.

in   d  3 ft  24 in   3 ft  12  ft    60 in The answer is (D).

option C

in   12db  3 ft  12 1 in    3 ft  12  ft    48 in STRC ©2015 Professional Publications, Inc.


48

48




Development and Splice Length of Reinforcement positive moment reinforcement The steel area extends a minimum of 6 in into the support as shown.

Fig. 1.21 Positive Moment Reinforcement



49

49




Development and Splice Length of Reinforcement positive moment reinforcement (continued) Fig. 1.21 Positive Moment Reinforcement

bar size required such that • for beam framing into girder, ACI Eq. 12‐5

• for beam framing into column,

• at point of inflection,



50

50




Development and Splice Length of Reinforcement negative moment reinforcement

Fig. 1.22 Negative Moment Reinforcement

The steel area extends beyond PI as shown.



51

51




Development and Splice Length of Reinforcement splices in tension lap splices • may not be used for bars larger than #11 or bundled bars • in flexural members, transverse spacing between splices may not exceed 1/5 lap length or 6 in



52

52




Development and Splice Length of Reinforcement splices in tension (continued) Table 1.6 Tension Lap Splices

class A splice • may be used when both • As ≥ (2)(area required) • ≤ ½ of total reinforcement is spliced within 1 lap length • else, class B is required



53

53




Development and Splice Length of Reinforcement splices in tension (continued)

Fig. 1.23 Value of cs for Lap Splices

• • minimum length = 12 in • all modifiers used to calculate ld except for Ext • cs values used for calculations as shown



54

54




Development and Splice Length of Reinforcement Fig. 1.24 Value of cs in Slabs and Walls



55

55




Development and Splice Length of Reinforcement splices in compression • length of splice (minimum 12 in)

• increase length by 33% if fc’ < 3 ksi When bars of different diameters are spliced in compression or in tension, use larger value of • splice length of smaller bar • development length of larger bar STRC ©2015 Professional Publications, Inc.


56

56




Development and Splice Length of Reinforcement splices in compression (continued) Column lap lengths may be reduced by • 17% when ties are provided with an effective area of 0.0015hs • 25% when spirals are used



57

57




Development and Splice Length of Reinforcement splices in compression (continued) • For columns that see tension, a class A tension lap splice is adequate if all of the following are met. • tension stress ≤ 0.5fy •

≤ ½ of bars spliced at same location

•

alternate splices are staggered by ld

• Otherwise, use a class B tension lap splice.



58

58



Reinforced Concrete Design Example: Development and Splice Length of Reinforcement Under extreme load cases, a column sees negligible tension forces. What sort of splice is required for the longitudinal reinforcement? (A) compression splice (B) class A tension splice (C) class B tension splice



59

59



Reinforced Concrete Design Example: Development and Splice Length of Reinforcement Under extreme load cases, a column sees negligible tension forces. What sort of splice is required for the longitudinal reinforcement? (A) compression splice (B) class A tension splice (C) class B tension splice The answer is (C).



60

60




Two‐Way Slab Systems design techniques types of slab systems

design methods for two‐way slabs

• one‐way slabs

• direct design method

• two‐way slabs

• equivalent frame method

• flat plates

• yield line method

• flat slabs • waffle slabs



61

61




Two‐Way Slab Systems Fig. 1.26 Details of Design Strips

direct design method • See STRM or ACI Sec. 13.6.1 for conditions of applicability. • divide slab into design strips as shown



62

62




Two‐Way Slab Systems design for flexure • total factored static moment ACI Eq. 13‐4

• Determine the positive and negative moments as shown in Fig. 1.27 (on next slide).



63

63




Two‐Way Slab Systems Fig. 1.27 Mo Distribution Factors



64

64




Two‐Way Slab Systems design for flexure (continued) • Positive and negative moment are distributed to strips based on relative stiffness. • Stiffness is determined using equivalent dimensions as shown in Fig. 1.25.



65

65




Two‐Way Slab Systems Fig. 1.25 Equivalent Beam and Slab Dimensions

αf

= ratio of flexural stiffness of beam section to flexural stiffness of a slab width bounded laterally by center lines of adjacent panels (if any) on each side of the beam = EcbIb/EcsIs

ln

= length of clear span in direction that moments are being determined, measured face‐to‐ face of supports = l1−c1 > 0.65l1

Is

= moment of inertia about centroidal axis of gross section of slab = h3/12 times width of slab defined in symbols α and βt STRC ©2015 Professional Publications, Inc.


66

66




Two‐Way Slab Systems design for flexure (continued)

Table 1.8 Percentage Distribution of Exterior Negative Moment to Column Strip

• Distribute moments to strips as shown in STRM Table 1.7 – Table 1.9. • The remaining moment is sent to the middle strip. Table 1.7 Percentage Distribution of Interior Negative Moment to Column Strip

Table 1.9 Percentage Distribution of Positive Moment to Column Strip



67

67




Two‐Way Slab Systems design for flexure (continued) Edge beam moments are shown in STRM Table 1.10.

Table 1.10 Percentage Distribution of Column Strip Moments to Edge Beam



68

68




Example: Two‐Way Slab Systems CSCO Example 8.2



69

69




Example: Two‐Way Slab Systems



70

70




Example: Two‐Way Slab Systems CSCO Example 8.3



71

71







72

72







73

73







74

74







75

75




Two‐Way Slab Systems design for shear

Fig. 1.28 Critical Sections for Shear

must consider both • flexural (one‐way shear) • punching (two‐way shear)



76

76




Two‐Way Slab Systems design for shear (continued) • flexural shear capacity (parallel to l1)

• critical perimeter for punching shear • interior column • edge and corner column (Fig. 1.29) • reduction for openings (Fig. 1.30) STRC ©2015 Professional Publications, Inc.


77

77




Two‐Way Slab Systems Fig. 1.29 Corner and Edge Columns

Fig. 1.30 Reduction in Critical Perimeter



78

78




Two‐Way Slab Systems design for shear (continued) punching shear capacity ACI Eq. 11‐33 ACI Eq. 11‐31

ACI Eq. 11‐32



79

79




Anchoring to Concrete code requirements • governed by ACI App. D as amended by IBC Sec. 1905.1.9 • transmission of loads by tension, shear, or a combination of both



80

80




Anchoring to Concrete code requirements (continued) Fig. 1.32 Tensile Failure Modes



81

81




Anchoring to Concrete code requirements (continued) Fig. 1.33 Shear Failure Modes



82

82




Anchoring to Concrete code requirements (continued) IBC Sec. 1905.1.9 modifies ACI as follows. • design strength of concrete = 0.75ϕNn and 0.75ϕVn (assuming concrete cracked) • strength of connection governed by steel or ductile attachments (For exceptions, see STRM or IBC Sec. 1905.1.9.)



83

83




Anchoring to Concrete anchor bolts in tension (steel strength of anchor) • nominal strength • tensile strength

• strength reduction factor



84

84




Anchoring to Concrete anchor bolts in tension (single anchor concrete breakout strength)

Fig. 1.34 Concrete Breakout of Anchor in Tension

• for single anchor away from edges of concrete, projected area = • for single anchor close to edge, reduced area = ANc • nominal breakout strength



85

85




Anchoring to Concrete anchor bolts in tension (single anchor concrete breakout strength, continued) nominal breakout strength modification factors • edge effects when • edge effects when • cracked concrete

• post‐installed anchors



86

86




Anchoring to Concrete anchor bolts in tension (single anchor concrete breakout strength, continued) • basic breakout strength

• when

• coefficient for concrete breakout strength

• For normal weight concrete, • strength reduction factor



87

87




Anchoring to Concrete anchor bolts in tension (multiple anchor concrete breakout strength)

Fig. 1.35 Concrete Breakout Surface for an Anchor Group

projected area (shown in Fig. 1.35)

n = number of anchors in the group a = distance between outside anchors in the group b = distance between outside anchors in the group perpendicular to a STRC ©2015 Professional Publications, Inc.


88

88




Anchoring to Concrete anchor bolts in tension (multiple anchor concrete breakout strength, continued)

Fig. 1.35 Concrete Breakout Surface for an Anchor Group

• nominal breakout strength

• eccentric loading modification factor




89

89




Anchoring to Concrete anchor bolts in tension (pullout strength of anchor) • nominal strength (typical) ACI Eq. D‐13

• nominal strength (headed bolt of stud) ACI Eq. D‐14

• nominal strength (hooked bolt)

N p  0.9 f c eh d a

ACI Eq. D‐15

• cracked concrete modification



90

90




Anchoring to Concrete anchor bolts in tension (side‐face blowout strength of anchor) • nominal strength

• If ca2 < 3ca1, the value Nsb is multiplied by the factor (1 + ca2 / ca1)/4, where 1.0 ≤ ca2 / ca1 ≤ 3.0. • only applicable when hef > 2.5ca1



91

91




Anchoring to Concrete anchor bolts in tension (concrete splitting) unless supplementary reinforcement is provided to control splitting • minimum center‐to‐center spacing of anchors • 4da (untorqued cast‐in anchors) • 6da (torqued cast‐in anchors) • minimum edge distance • same as normal cover requirements (untorqued cast‐in anchors) • 6da (torqued cast‐in anchors)



92

92




Anchoring to Concrete anchor bolts in shear (steel strength of anchor) • nominal strength of headed stud, • nominal strength of headed bolt and hooked bolt, • specified tensile strength of anchor

• strength reduction factors

fya = specified yield strength of the anchor STRC ©2015 Professional Publications, Inc.


93

93




Anchoring to Concrete anchor bolts in shear (single anchor concrete breakout strength)

Fig. 1.34 Concrete Breakout Surface in Shear

• projected area of failure surface ca1 = distance from center of anchor rod to edge of concrete in the direction of the shear force • when failure surface is limited by edge of concrete, reduce projected area by Avc



94

94




Anchoring to Concrete anchor bolts in shear (single anchor concrete breakout strength, continued) nominal strength



95

95




Anchoring to Concrete anchor bolts in shear (single anchor concrete breakout strength, continued) modification factors • edge effects

• member thickness (ha < 1.5ca1)

• cracked concrete



96

96




Anchoring to Concrete anchor bolts in shear (single anchor concrete breakout strength, continued) • basic concrete breakout strength (smaller of)

• le = load bearing length of anchor for shear (≤ 8da in all cases) • hef = for anchors with constant stiffness over embedded section



97

97




Anchoring to Concrete anchor bolts in shear (multiple anchor concrete breakout strength) • projected area, ha ≤ ca1

Fig. 1.37 Concrete Breakout Surface for an Anchor Group in Shear

when limited, modify projected area by AVc • nominal strength



98

98




Anchoring to Concrete anchor bolts in shear (multiple anchor concrete breakout strength, continued)

Fig. 1.37 Concrete Breakout Surface for an Anchor Group in Shear

• eccentricity modification factor




99

99




Anchoring to Concrete concrete pryout strength of anchor in shear • nominal strength (single anchor)

• pryout coefficient

• nominal strength (group of anchors)



100

100




Anchoring to Concrete interaction of tensile and shear forces • When Vua ≥ 0.2ϕVn and Nua ≥ 0.2ϕNn, the interaction expression of ACI Eq. D‐42 applies.

ϕNn = governing tensile capacity ϕVn = governing shear capacity • When Vua < 0.2ϕVn, neglect shear effects and design strictly for tension. • When Nua < 0.2ϕNn, neglect tension effects and design strictly for shear.



101

101




Example: Anchoring to Concrete An anchor bolt has a governing tensile capacity of 10 kips and a governing shear capacity of 20 kips. Is the bolt acceptable under an applied live load of 6 kips tension and 3.5 kips shear?



102

102





Determine the factored loads and compare to 20% governing capacity. 0.2 N n   0.2 10 kips   2 kips N u  1.6  6 kips   9.6 kips

consider tension  0.2Vn   0.2  20 kips   4 kips Vu  1.6  3.5 kips   2 kips

 5.6 kips  4 kips STRC ©2015 Professional Publications, Inc.


consider shear  103

103





Since both tension and shear must be considered, use the interaction equation. Nu V  u  1.2  N n Vn 9.6 kips 5.6 kips   1.2 10 kips 20 kips 1.24  1.2



 unacceptable

104

104




Lesson Overview Reinforced Concrete Design (Part 2) • Concrete Columns • Development and Splice Length of Reinforcement • Two‐Way Slab Systems • Anchoring to Concrete



105

105




Learning Objectives You will learn • R/C column design • R/C slab design • design of anchorage to concrete • how to avoid potential SE exam pitfalls • tricks to speed up problem solving on the exam



106

106

STRC02 ReinforcedConcrete Part2 0715

Recommend Documents